Talk:Schwarz lantern/GA1

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Reviewer: Ovinus (talk · contribs) 19:22, 10 June 2022 (UTC)[reply]

Comments:

  • In the lead, it'd be nice to put the Schwarz lantern in context (contrasting it with 1-dimensional behavior). Maybe in the sentence with "demonstrates that", could just add something like "unlike with the approximation of curves by line segments" set off by commas Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
Writing that, I see that you do so in the next section. I still think it's important enough to put in the lead, though? Esp. because it's not too hard to explain Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
  • Ok, added to lead. I also removed some footnotes from the lead, leaving only the ones on naming that were not summaries of later body content. —David Eppstein (talk) 01:38, 11 June 2022 (UTC)[reply]
  • "provides an analogous counterexample" – Is the counterexample really just analogous, given the points are on the curve? I'd say maybe "analogous, but stronger", something like that Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • Well, I think it's analogous, but I suppose that's an unsourced editorialization. It doesn't really add much to the actual content. Readers can decide for themselves whether they think it's analogous. Removed. —David Eppstein (talk) 01:44, 11 June 2022 (UTC)[reply]
  • "Other sources may use different parameterizations; for instance" – materially different parameterizations, or simply conventions? Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • I don't know, are linear transformations such as halving the triangles-per-ring parameter or counting circles instead of the rings cut by the circles materially different? —David Eppstein (talk) 20:25, 10 June 2022 (UTC)[reply]
      • Ah, okay. It's just the example in the footnote is only using a different letter, which is definitely not a different parametrization. No problem, then. Ovinus (talk) 23:29, 10 June 2022 (UTC)[reply]
  • "having normals far from the surface it is intended to approximate" – A bit funky; I think you mean "having normals far from the surface normals they are intended to approximate" Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
  • I'd restructure the stuff including and following "Basic forms of the finite element method..." to be in a separate paragraph, and putting first the 180° thing about the lantern specifically (that is, "Schwarz lanterns whose triangles' angles are bounded away from 180° ..."). Rationale: That is easier to understand irrespective of any knowledge of numerical methods and is more general. Plus it's immediately followed by its application to the real world. Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
  • I'd say somewhere, since you invoke topological equivalence, that the lantern converges both pointwise and uniformly Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • Mentioned uniform convergence at the start of the limits section. This was a little more difficult to source than I expected but I found a new source saying so. Since uniform automatically implies pointwise is it really necessary to say that it also converges pointwise? Anyone who understands that distinction will already make that inference. —David Eppstein (talk) 20:49, 10 June 2022 (UTC)[reply]
      • Great, and agreed w/ the inference Ovinus (talk) 23:29, 10 June 2022 (UTC)[reply]
  • "a flat plane" – vs. a curved plane? :P Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
  • "can be folded out of a flat piece of paper" – perhaps link developable surface, although thatmight be an easter egg Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • I'm not convinced that's helpful, because developable surfaces (at least as discussed at that link) are smooth rather than folded. —David Eppstein (talk) 20:33, 10 June 2022 (UTC)[reply]
      • Ah, TIL that smoothness was a requirement. Ovinus (talk) 23:29, 10 June 2022 (UTC)[reply]
  • "resulting surface will have a seam rather than forming a continuous cylinder" – I think this is being somewhat pedantic, no? Is the point the implication that the paper and the cylinder aren't topologically equivalent? Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • Ok, removed mention of the seam. Right, you'll get a lengthwise cut down the cylinder. But for the purposes of understanding the shape and its area I guess that's irrelevant. —David Eppstein (talk) 01:47, 11 June 2022 (UTC)[reply]
  • "sagitta of the arc" – Never heard this word; maybe put a footnote of what the sagitta is? Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • Isn't that what the wikilink is for? Anyway footnotes are cheap so I added one. —David Eppstein (talk) 20:25, 10 June 2022 (UTC)[reply]
  • Are there generalizations to hypervolume approximation by simplices? Ovinus (talk) 19:22, 10 June 2022 (UTC)[reply]
    • Presumably there are appropriate definitions for how to approximate hypervolume by simplices without running into errors like this case. Whether there are higher-dimensional generalized counterexamples that people have used widely to debunk bad attempts at definitions is a different question. I don't know of such examples and didn't run into any when digging up sourcing for this article. —David Eppstein (talk) 20:33, 10 June 2022 (UTC)[reply]
  • Admittedly this is being pedantic, but wouldn't it be possible for the area to neither diverge to infinity, nor converge, for a particularly malicious choice of the relation between m and n (and oscillate, for example)? Ovinus (talk) 05:19, 11 June 2022 (UTC)[reply]
    • I think so. But we don't have sources that say so. That's still diverging, isn't it? Just not diverging to infinity. —David Eppstein (talk) 06:15, 11 June 2022 (UTC)[reply]

All looks good. Passing. Ovinus (talk) 15:11, 11 June 2022 (UTC)[reply]

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